There has been a lot of talk about this so I'll input my 2 cents. I've been here for 4 years, now doing HR related things and I have to go through hundreds of resumes a week, so I hope you all read this before applying to any job in China!
If you are planning to work in China, get a working Z visa. It is legally required. If you are caught working without one, you will be fined, detained, then deported. The company you are illegally working for will also be fined, and possibly shut down, because they are not paying tax on you.
To get a Z visa as an English teacher, you must have these requirements. The Chinese government will not issue you a Z visa without them. Note, these are updated as of February 2014. I didn't make these rules, don't get angry at the messenger.
1st - Must be a native English speaker, and have a passport/citizenship card from a Native English speaking country (sorry India, English as an official language doesn't count.)
2nd - Must have a university or college degree. Sometimes an associates degree works, bachelors always.
3rd - New law, must have a teaching certificate, such as TEFL or TESOL.
If you cannot fulfill these requirements, the Chinese immigration office will not issue you a Z visa to be an English teacher. DO NOT COME ON ANY OTHER VISA, EXPECTING TO SWITCH TO A Z VISA. If you come to China on any other visa, you need to LEAVE China to get a Z visa. You can do this two ways - go back to your home country (preferred,) or you can leave China, ship all your documents to your home country, have someone there go to the Chinese embassy, and ship it back to wherever your taking your vacation. As long as the exit stamp, visa date, and entry date all work out, it should be fine.
If you have any more questions about this, please feel free to ask!